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Breaking time for the quantum chaotic attractor.

A Iomin¹, G M Zaslavsky

¹Department of Physics, Technion, Haifa 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 15, 2003

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This study examines quantum dissipative systems where classical limits show chaotic attractors. Researchers found that the breaking time of classical-quantum correspondence can be arbitrarily large for dying attractors.

Area of Science:

Quantum physics
Chaos theory
Statistical mechanics

Background:

Classical-quantum correspondence is crucial for understanding physical systems.
Dissipative systems and chaotic attractors present unique challenges in quantum mechanics.
The breaking time of classical-quantum correspondence indicates the limits of classical descriptions.

Purpose of the Study:

To investigate the breaking time of classical-quantum correspondence in a quantum dissipative system.
To analyze a model exhibiting a chaotic attractor in its classical limit.
To explore the influence of dissipation on the classical-quantum correspondence.

Main Methods:

A theoretical model of a periodically kicked harmonic oscillator with dissipation was developed.

Related Experiment Videos

The model was analyzed in the regime where the classical limit corresponds to a chaotic attractor.

The breaking time, tau(Planck), of classical-quantum correspondence was mathematically derived.

Main Results:

The study obtained the breaking time, tau(Planck), for classical-quantum correspondence.
It was demonstrated that tau(Planck) can be arbitrarily large in the limit of a dying attractor.
The model serves as an analog for the dissipative kicked Harper model.

Conclusions:

The breaking time of classical-quantum correspondence in dissipative chaotic systems is sensitive to attractor properties.
The concept of a 'dying attractor' allows for an extended validity of classical descriptions in quantum systems.
This research provides insights into the boundary between classical and quantum physics in dissipative chaotic regimes.